Lozenge Land
Read a flat tiling as deep stone, and cut the cheapest stairs that let the water climb it.
- Grades
- 3–6
- Subjects
- Shapes & Space, Logic
- Kind
- Puzzle
- Cost
- Free, no account, no ads
What it is
The board is a tiling of three kinds of rhombus, and it is also a heap of stone blocks seen from one corner: pale floors, a sunlit wall and a shaded one. Tap a corner where all three kinds meet and a block pops out, or back in. Water starts on the lowest floor and climbs any step of one block, but a drop of two is a cliff it cannot get up. Every floor it reaches turns to grass. Cut stairs, or shave stone away, until the whole land is green, changing no more blocks than the aim allows.
What it gives you to practise
Seeing depth in a flat drawing, and holding on to it. The same rhombuses read as a heap or as a hollow, and the trees standing on the floors are there to say which way is up. Then planning: a block can only sit where the blocks behind it and beside it hold it up, so the cheapest stair is rarely the first one that comes to mind. On every chosen board the aim is the true minimum, proved by a computer that tried every carving of that stone, so matching it is a real result.
In a classroom
The board prints as line art with the grass taken off, so finding where the water stops becomes the paper puzzle and a pencil marks the blocks to change. The first stones in Level I need a block or two; a couple of those, before anybody tries a ten-across stone, is enough for a class to agree on which way is up.
The rules
Cut stairs until the water reaches every floor.
Tap a corner where all three kinds of face meet: a block pops out of the stone, or back in.
Water starts on the floor nearest you and climbs a step of one block. Two blocks is a cliff, and it stops.
Build a step, or shave one off — in as few blocks as the aim says.
Every aim on a chosen stone is the true best: no carving of that stone waters it in fewer. On Level III's wild stones the aim is the best the machine itself could plan — match it, or beat it.
Near it on the shelf
- Balanced ZebraBoth colours have to multiply out to the same number, and then to the largest that shape allows.
- Fractured FractionsOne point cuts the whole picture at once, and every piece has to come out holding the fraction written on it.
- Hitome's GardenEvery line has just two ways to go, and the walls they make decide which flowers end up sharing a bed.